First let me say that troubleshooting and repairing these amps yourself from inside is extremely difficult unless you are an experienced tech/engineer. They are not hand wired point to point jobs from the '60s stone age, (my era! ), they are modern high quality electronic units built to full modern specs and all the better for it.

Some other useful info would be to know does it do it on all channels with the boost both on and off?

Things you could actually try are to replace each valve in turn with a known good version. The EL84s should really be replaced as a pair if possible though it would not be disastrous if you couldn't just for the purpose of testing, (the inner two and outer two are the matched pairs). DO NOT just replace them all in the hope that that will cure it, it will not tell you which valve (if any) is faulty. Borrow a 12AX7 and an EL84 from another amp, a fellow band member's has to be favourite, and use it in each spot in turn. Once you have identified any valve problem you can then replace just the one or the pair you need to if you prefer. That way you would keep as much of your existing sound as you are able assuming you like it. Make sure to put the valves back in their original locations if they are found to be good!

Other than that the rest is in trying simple things to locate whereabouts in the circuit the problem is occurring. You should introduce a signal into the Fx Return with a standard guitar cable and see if the level still goes up and down. This can be from another amp's Fx Send or from a guitar or maybe even a music source if you are able. Start with the amp's Master Volume fully down! If the problem vanishes then it is before the Fx Loop and if it remains it is in the power stages after the Fx loop. You can also try to take the signal out of the Fx Send into another amp's Fx Return loop to do the same thing in reverse and confirm where it happens.

If possible try taking the signal from the Redbox into another amp or mixer and see if it still does the same. If it doesn't then your problem is most likely in the power soak area as the Redbox takes its signal from the input to that.

EDIT: If you can do the valve swap testing, do you know the correct procedure for removing the enclosure top to get at the valves without nullifying the warranty tags?

I don't know the valve removal procedure but I don't have a warranty right now anyhow it has run out. But I have seen a few YouTube videos showing what you are describing so I will do it that way. Thank you for all the information I appreciate it. So I will try to work through all the steps you described. I am not any type of tech but I'm a high voltage electrician so I have some knowledge but I really know very very little about amps low voltage and small circuitry.

Don't let me make you think the procedure for opening up the amp is complicated, it isn't. It's just that there are a couple of tags on the lower screws on the inside and if the screws are fully removed these are damaged and show that to H&K. You just need to remove completely the two top screws and the rear handle screw on each end cap. Do not touch the front handle screw, that only holds the handle onto the end cap. You then loosen the bottom two screws on each end only a couple of turns. Just enough in fact to allow the end caps to lean outwards. The enclosure top can then be removed as a single unit.

Keep an eye out for the front panel LED pcb strip which sits under the front lip of the enclosure lid. Be careful you don't stretch the wiring to it from the lower chamber under the valves. Make sure to refit that correctly with its clips in place before you put the lid back on again.